Amnesty International has written to every member of the House of Lords urging them to oppose government plans that it says will prevent victims of human rights abuses overseas suing UK multinational companies.

So far this week the government has been defeated six times in the Lords over amendments to the legal aid, sentencing and punishment of offenders bill, which aims to save £350m a year from the Ministry of Justice budget.

Further votes are due next week on reform of the "no win, no fee" system that the justice secretary, Kenneth Clarke, has attacked for fuelling a "compensation culture".

Amnesty warns that the bill will require both the lawyer's success fee and the after the event insurance premium to be paid for out of the compensation awarded to victims.

"Taken together, these costs are likely to wipe out potential damages awarded and will make the claim financially unviable at the outset," Amnesty says.

"Under the proposed reforms, it is unlikely that victims such as the 69,000 people living in Bodo, Nigeria, would have been able to pursue a case against the multinational conglomerate Shell, who recently admitted full culpability for two massive oil spills in the region."

Kate Allen, director of Amnesty International UK, said: "It is outrageous that a government which professes to want to promote 'responsible capitalism' is giving carte blanche to powerful goliath companies to abuse human rights with no remedy for their victims.

"The proposed reforms will not even come with a saving to the public purse. The only beneficiaries will be the multinational corporations defending the case whose costs will be reduced at the expense of the victims' damages. This should not be allowed to happen."

The government is trying to turn the battle over the bill into a party political dispute, with David Cameron taunting the Labour leadership that it is opposed to any financial cuts and as financially irresponsible as Greek parliamentarians.

Campaigners opposing the bill point out that many of the amendments in the Lords have been put down by Conservative peers such as Lord Newton, a former social security minister under Margaret Thatcher, Liberal Democrat and crossbench peers. Even the Taxpayers' Alliance has expressed concern about the proposals.

On Wednesday night, the Lords voted by 237 to 198 to preserve legal aid for appeals against welfare benefit decisions, defeating reforms in the government's bill.

The amendment had been tabled by the Liberal Democrat Lady Doocey with support from Labour, Conservative and cross-bench peers.

A second amendment, tabled by Lord Newton, ensured that legal aid should be available for higher-tier benefit appeals. It was passed by 222 votes to 194.

On funding medical reports for clinical negligence cases, the government was beaten by 178 to 172 votes. An attempt to retain legal aid for all medical negligence cases, however, did not succeed.

The votes came at the end of a two-hour debate during which every speaker in the upper chamber – apart from the minister – opposed the Ministry of Justice plans. Peers from all parties questioned whether the proposed savings would be made.

Earlier Lord McNally, the Liberal Democrat justice minister, warned that if the government lost on the issue of providing legal aid on welfare benefit issues and support for advice centres, it would "tear out the heart of the rationale of the bill".

The defeats will add to the pressure on the government's parliamentary timetable. On Monday, the government was defeated on three other legal aid amendments.

The coalition is expected to try to reverse the Lords' decisions in the House of Commons on the grounds that the bill is primarily a financial measure.

Commenting on the vote to retain legal aid for welfare benefit appeals, the shadow justice secretary, Sadiq Khan, said: "This victory provides a vital safety net for the poorest in our society. It ensures that when bureaucrats make a mistake which denies support, like disability benefits, to the vulnerable and their families, then they will have expert advice in making an appeal.

"According to Citizens Advice, every £1 of taxpayer money spent on legal aid in benefit cases saves the state up to £8.80 down the line. So, regardless of the government's spin, today's vote is also about saving the taxpayer money through early-stage intervention, of the kind that prevents problems escalating, reducing the call on resources, in future months and years."

Richard Hawkes, chief executive of the disability charity Scope, said: "Thousands of disabled people and their families will be delighted at the action taken by peers in the House of Lords today.

"The Lords have recognised that to cut legal aid at a time of unprecedented changes to welfare support would have meant disabled people who fall foul of poor decision-making, red tape or administrative error would have been pushed even further into poverty as they struggled to manoeuvre the complicated legal system without the necessary expert support they need.

"The result would have been a ticking time-bomb of poorly prepared and lengthy tribunals and appeals, choking the courts and not saving money as suggested by Ken Clarke, but actually costing the government far more in the long term."